Answer :
The greatest 3-digit base 8 positive integer that is divisible by 5 is 777.
What is divisibility?
A divisibility rule is a convenient shorthand for checking if an integer is divisible by a given set divisor without actually doing the division, typically by looking at the digits of the number.
Here,
The smallest number that has 3 digits in base 8 is 8² = 64
= 100(base 8).
In fact, in base 8 you would write the calculation as 10² = 100.
The largest 3-digit base 8 number is 777
= 10³ - 1. In base 10 it's 8³ - 1 = 511.
The base does not affect divisibility.
= 512 / 5 = 102 remainders 2,
so there are 102 multiples of 5 less than 512.
These 102 numbers have 3 or few digits.
= 64 / 5 = 12 remainders 4.
There are 12 multiples of 5 less than 64.
These have 1 or 2 digits.
So the number of multiples of 5 between 64 and 511 is 102 - 12 = 90. These numbers have exactly 3 digits.
Hence, the greatest 3-digit base 8 positive integer that is divisible by 5 is 777.
To learn more about the divisibility from the given link
https://brainly.com/question/9462805
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